I don't exactly know about a stove. And not really about quail either. But apparently it is relatively common that parrot owners suddenly loose their parrots due to fumes - and carbon monoxide, which I suspect is the most likely, dangerous fume to come from your stove, is one of the possible culprits. And it is very dangerous to people too, birds are just more sensitive to it - and to fumes in general - so if carbon monoxide poisoning is at all possible, I wouldn't put a fire in that stove again without having a carbon monoxide detector ready or at least having thoroughly cleaned the chimney.
Another parrot killer is self cleaning ovens - I'm not aware what exact fume is the cause, but I've read several stories about birds dying because the owner turned on the self cleaning function - even if the birds were in another room.
Non-stick cookware is apparently a problem as well, as it can release fumes if over heated, and those also kill parrots quickly.
Your story sounds a lot like the parrot-stories I've read, you don't mention any prior problems with the birds and finding one of them alive and have it die in your lap a few minutes later is really the typical parrot-killed-by-fume story.. Only alternative theory I have is boinking, but I don't assume that's a possibility. And having two boink to death at the same time doesn't sound very likely either.